On projective motions of five-dimensional spaces of special form

Abstract

The paper is devoted to the problem of determining of 5-dimensional pseudo-Riemannian manifolds (M, g) admitting projective motions (h-spaces). A similar problem for n-dimensional proper Riemannian and Lorentz spaces was solved by Levi-Civita, Solodovnikov, Petrov and Aminova. For pseudo-Riemannian manifolds of arbitrary signature and dimension the problem of their classification in Lie algebras and Lie groups of projective transformations, set more than a hundred years ago, is still open. In this paper five-dimensional h-spaces of the type {221} are determined using the method of skew-normal frame (Aminova) and necessary and sufficient conditions for the existence of projective motions of the same type are established.